G. P. (George Payn) Quackenbos.

A natural philosphy: embracing the most recent discoveries in the various branches of physics .. online

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and increases his stability still further by using a cane.

When attempting to rise from a sitting position, a man
must either bend his body forward or draw his feet back-
ward, in order to bring his centre of gravity over his base;
otherwise, he will fall back in making the attempt. So, a
person who keeps his heels against a wall, can not stoop
without falling, because he has no room to throw the mid'
die of his body far enough back to keep the line of direc^
tion within the base.



Nature teach-
es a man when de-
scending a height
to lean backward,
and when ascend-
ing to lean for-
ward, as shown in
Fig. 71. In like
manner, when
carrying a weight
on one side, we

sway our body to the other, like the man with the
watering-pot, in Fig. 72. "We find it easier to
carry a pail of water in each hand than to carry
but one, because the weights balance each other,



Fig. 72.





KiG Where does the centre of gravity lie in a man's body ? How may a man increase
his stability ? When attempting to rise from a sitting position, what must a man do ?
Why can not a person stoop, if he keeps his heels against a wall ? What does nature
teach a man to do, when, descending a height? When ascending a height? When



MECHANICS.



and no effort is necessary to keep the line of direction within the
base.

An infant that has not learned to balance itself in a standing position
creeps on all fours without danger, because it thus brings its centre of grav-
ity lower and enlarges its base. In order to walk, it must know how to pre-
serve its balance ; and, as some practice is necessary for this, the child in its
first efforts is likely to fall. The same is the case with a dizzy or an intoxi-
cated person, who for the time loses the power of preserving his balance
that is, of keeping his line of direction within his base.

167. When a person slips on one side, he naturally throws out his arm on
the other. He thus seeks to bring back his centre of gravity over his base,
and, when he can do so, he saves himself from falling. A person skating has
to use his arms constantly for this purpose. Rope-dancers, in performing



Fig. 73.



their feats, have to shift their centre
of gravity from point to point with
great rapidity ; and, finding their
arms insufficient for maintaining
their balance on the rope, they use
a long pole, with a slight motion of
which they can throw the centre of
gravity into any desired position.

168. The shepherds of Landes
[lond], in the south-west of France,
have turned the art of balancing to
good account. Having to tend their
sheep in a region covered with marsh
in winter and hot sand in summer,
they mount on stilts about four feet
high. Though the centre of gravity
is raised, and their liability to fall
thus increased, by practising from
an early age they become exceeding-
ly expert on these stilts, and can not
only walk on them, but even dance,
and run so fast that it is hard for a
stranger to keep up with them.

169. STABLE AND UNSTABLE EQUILIBRIUM. The centre
of gravity of everybody tends to get to the lowest possible
point.

carrying a weight on one side ? Why do we find it easier to carry a pail of water in

each hand thjCn to carry but one ? Why is an infant safer when creeping than when

t attempting to walk ? Why does an intoxicated person reel? 167. When a person

' slips on one side, what does he do, and why ? How do rope-dancers preserve their

balance ? 168. How have the shepherds of Landes turned the art of balancing to

practical use ? 169. What point does the centre of gravity tend to reach ? Illustrate




SHEPHERDS OF LAJCDES.




STABLE AND UNSTABLE EQUILIBEIUM. 79

A ball suspended by a string, as in Fig. 74, and re- Fig. 74.

leased from the baud at K, or any otber point, will not
come to rest till it reaches L, because there its centre
of gravity, B, is at its lowest point. Hence, when a
pendulum or plummet comes to rest, it always hangs
vertically.

A hammer, no matter in what way it is thrown up,
descends with its iron part first, because the centre of
gravity, which is in that part, tends to get as low as
possible. For the same reason, a shuttlecock or an
arrow, when it has reached its highest point, turns
and descends with its heaviest part foremost.

170. A solid body resting on a surface in such a way
that its centre of gravity is lower than it would be in any
other position, is said to be in Stable Equilibrium. If its
centre of gravity could be brought lower by placing it dif-
ferently, it is said to be in Unstable Equilibrium.

Fig. 75. Thus, the oval body, A B, represent- Fig. 76.

ed in Fig. 75, is in stable equilibrium, s^~~\
because its centre of gravity, C, is at / \

its lowest possible point ; and a force
applied to either end will not cause it
to fall over, but only to rock to and fro.

In the position shown in Fig. 76, it is in unstable equilibrium,
because its centre of gravity might be brought lower ; and a
slight push will overturn it and bring it to the position shown in Fig. 75. It
is hardly possible to balance an egg on either end ; but placed on its side, it
rests securely.

171. The stability of a sphere, or oval body like an egg,
is increased by cutting it into two equal parts, as shown in
Fig. 77. Bases of this shape are Fi<y 7T

used in rocking toys, for support-
ing the figures of men and animals.
Of this shape, also, are some of the
huge Rocking Stones found in different parts of Europe,
which are so nicely poised that the slightest push causes'
them to rock to and fro, while a dozen men can not over-
turn them.

this with Fig. 71. When a pendulum or plummet comes to rest, how does it ban??
How docs a hammer, a shuttlecock, or .an arrow, descend, when thrown up into the
air, and why ? 170. When is a body said to be in Stable Equilibrium ? Whon, in Un-
stable Equilibrium ? Apply this in Figs. 75 and 76. 171. How may the stability of a




80



MECHANICS.



Fig. 7a



172. PARADOXES. The tendency of the centre of Grav-
ity to reach its lowest possible point sometimes produces
wonderful effects, or Paradoxes, for which the unlearned
are at a loss to account. Thus, we know that a ball will roll
down a sloping surface ; but a ball of light wood may be
made to roll up a sloping surface by inserting a piece of
lead in one side.

The ball A, for instance, loaded on
one side with a plug of lead S,is placed
on a sloping surface. The centre of
gravity C, which is nearS, at once tends
to reach its lowest point ; and owing to
this tendency the ball rolls, till it reaches
the position shown in B.

173. In like manner, a double cone, or
body having the form of two sugar-loaves joined at their large ends, may be
made to roll up an inclined plane. Fig. 79 represents two rails, joined at one

end, but apart and somewhat ele-
vated at the other. Place the
double cone at the middle of the
rails just described, and instead
of rolling down to the narrow end
it will roll up to the wide end.
" This is because the centre of grav-
ity, though apparently going up, is really going down ; for, as the rails di-
verge, they let the double cone further down between them.




Tig. T9.




sphere or oval body be increased ? For -what are bases of this shape used ? What
stones are of this shape ? 172. What are Paradoxes ? How are they sometimes pro-
duced ? How may a ball be made to roll up a sloping surface ? Explain the principle
involved, with Fig. 78. 1T3. Describe the experiment with tbe double cone, and ex-
plain the principle



MOTIVE POWERS. 81



CHAPTER VII.

MECHANICS (CONTINUED).

THE MOTIVE POWER. THE RESISTANCE. THE MACHINE.

STRENGTH OF MATERIALS.

174. IN a previous chapter we have treated of the Laws
of Motion ; we now proceed to consider the following prac-
tical points :

I. The Motive Power, or Force by which motion is pro-

duced.

II. The Resistance to be overcome, or work to be done,

which is always opposed to the Power.

III. The Machine, which is used by the Power in over-

coming the Resistance, when it does not itself di-
rectly act.

IV. The Strength of the Materials employed.

In the case of a steamboat, steam is the Power by which motion is pro-
duced ; the weight of the boat is the Resistance, which constantly opposes
the Power. Since steam can not be directly applied in such a way as to move
the boat, a Machine is used to aid in overcoming the Resistance ; and this
Machine is the engine. On the strength of the materials employed depend
the usefulness and safety of the whole.

Motive Power.

175. The chief powers used by man in producing mo-
tion are gravity, the elastic force of springs, his own
strength, the strength of animals, wind, water, and steam.

176. Gravity. Springs. Gravity is applied by attach-
ing weights to machinery, which they keep in motion by
their constant downward tendency, as in certain kinds of

174. What four subjects connected with Mechanics are treated of in the present
chapter? In the case of a steamboat, what is the power? What, the resistance?
What, the machine ? On what does the usefulness of the whole depend ? 175. Name
the chief powers employed by man in producin? motion. 170. How is gravity ap-



82 MECHANICS.

clocks. When the weight descends so far that it reaches a
support, the machinery ceases to move, and is said to " run
down". When there is no room to use weights, springs
are often substituted for them, as in the works of watches.
A spring is made of steel, or some other elastic substance ;
which, being bent, produces motion by a constant effort to
unbend itself.

177. Strength of Men and Animals. With his own
strength man can produce a certain degree of motion, but
not such as accomplishes the grandest results. From the
strength of animals he derives important assistance. Even
rude nations tame the animals around them, and turn their
strength to account. The American Indians, when first
discovered, had not learned to do this ; and therefore, like
other savages who rely entirely on their own strength, they
had made . no great advance in agriculture, manufactures,
or any other branch of industry.

The horse is the animal whose strength is most widely
and advantageously used. For continued labor, one horse
is considered equal to five men. A horse of average strength
can draw a load of a ton, on a good road, from 20 to 25
miles a day.

178. Wind and Water. Still more powerful forces are
found in wind and water, which are extensively used as
moving powers by all civilized nations.

The win'd is brought to bear, not only on the sails of vessels, but also in
mills used for grinding grain, sawing wood, raising water, expressing oil
from seeds, &c. Such machines are called Wind-mills ; they were introduced
into Europe from the East, about the time of the Crusades. The great objec-
tion to the wind as a moving power, is its irregularity, for in still weather the
machines it moves are useless.

Water is a very powerful and useful agent. A little stream is often a

plied ? When is the machinery said to run down ? When there is no room to use
weights, what are often substituted for them ? How does a spring produce motion ?
177 What is said of the strength of man as a source of motion ? What, of the
strength of animals ? What animal is most widely used ? To how many men is one
horse considered equal ? As regards drawing, what is a day's work for a horse of av-
erage strength ? 173. What sources of motion are still more powerful ? How is the
wind brought to bear? What are machines moved by the wind called? Whence
and when were wind-mills introduced into Europe ? What is the great objection to



STEAM, AS A MOTIVE POWEK. 83

source of prosperity and wealth to an extensive region. Affording what is
called " water-power ", it moves huge machines, and thus affords the means
of manufacturing easily and cheaply. Water was first used as a motive power
by the Romans, in simple machines for grinding grain, about the commence-
ment of the Christian era. It is now applied in various kinds of machines,
for sawing, spinning, weaving, grinding, &c. Though a stream may run so
high in spring and so low in summer as to be useless fox- a time, there is far
less diiliculty from these causes than from the irregularity of the wind.

179. /Steam. The greatest of all the powers employed
by man is STEAM, or the vapor generated by submitting
water to a high degree of heat. Steam being an elastic
fluid, its properties and applications will be considered
hereafter.

ISO. The uses of steam were unknown to the ancients ; it was not till near
the close of the seventeenth century that its importance began to be realized.
Its application to machinery marks an era in the world's history, and has in-
vested man with immense power over matter. Driving the boat and car, it
bears him what was once a day's journey in an hour. Applied in countless
varieties of machines, it is the means of supplying us with thousands of com-
forts unknown to our forefathers. The farmer is indebted to it for his spade,
doe, rake, scythe, ploughshare, and all his implements. It helps to make
the shears with which he cuts the wool from his sheep, and then cards the
wool, and weaves it into cloth. It separates his cotton from its seed, and
turns it into muslin and calico. It aids the builder by making his tools, forg-
ing his nails and bolts, moulding his ornaments, polishing his marble, cutting
his stone, and sawing his wood. It supplies our parlors with furniture, our
kitchens with cooking utensils, our dining-rooms with glass and china, knives
and forks. It knits, twists, washes, irons, dyes, gilds, grinds, digs, and
prints ; and hardly any work of art meets our eyes, in making which steam
lias not been directly or indirectly used. It does all this, moreover, with
wonderful precision and rapidity. The pyramids of Egypt, we are informed,
kept 100,000 men at work twenty years in their erection. It has been com-
puted that one powerful steam-engine would have done as much work in the
same time as 27,000 of these Egyptians.

TIac Icitaice.

181. Whatever opposes the Power is called the Resist-
ance.

the wind as a moving power? "What is said of water-power ? By whom and when
was it first used? For what purposes is it now employed? What are the disadvan-
tages of water as a moving power ? 179. What is the greatest of the powers em-
ployed by man ? What is Steam ? ISO. When did its importance begin to be real-
ized? What has been the result of its application to machinery? Enumerate the
different articles which steam is constantly employed in producing. What interest-



84 MECHANICS.

JL82. The resistance is not always of the same character.
It may be a weight to be lifted, as a pail of water from a
well ; or a body to be moved onward, as a train of cars ;
or a wheel to be turned, as in a mill ; or particles to be
compressed, as in packing cotton in bales ; or cohesion to
be overcome, as in splitting a log of wood. As the most
usual form in which the resistance appears is that of a
weight to be moved, the term Weight is often used instead
of Resistance, with reference to work of any kind, or what-
ever opposes the moving power.

183. UNITS OF WORK. The efficiency of a force is esti-
mated by the resistance it can overcome, or the amount of
work it can do. In order to compare different forces, we
must have a uniform unit of loork.

The unit of work adopted is the resistance encountered
in raising one pound through the space of a foot. Hence,
to raise a body any distance constitutes as many units of
work as there are pounds in the body multiplied by the
number of feet in the given distance. To raise 2 pounds
of water from a well 6 feet deep, is equivalent to twice 6,
or 12, units of work. To lift a load of 1,000 pounds 10
feet involves 10,000 units of work.

184. HORSE-POWERS. In estimating large amounts of
work, it is customary to use horse-powers as a measure. A
horse can perform 33,000 units of work, that is, can raise
33,000 pounds a foot, in a minute. An engine, therefore,
that can perform 33,000 units of work in a minute is said
to bean engine of one horse-power ; one that can do 63,000
units of work in a minute is an engine of 2 horse-powers ;
and so on. Hence the following

Rule. To find the horse-power of an engine, divide the
number of pounds it is capable of raising one foot in a min-
ute by 33,000.

Ing fact is stated with respect to the pyramids of Egypt? 181. What4s the Resist-
ance? 182. Mention some of the different forms in which the resistance appears, and
give examples. What term is often used instead of resistance, and why ? 183. How
Is the efficiency of a force estimated ? To compare different forces, what is it neces-
eary to have ? What is the unit of work generally adopted ? Give examples.



FRICTION. 85

185. FRICTION. The effect of the moving power is often
diminished by Friction.

Friction is the resistance which a moving body meets
with from the surface on which it moves.

If all surfaces were perfectly smooth, there would be no friction ; but even
those bodies that seein the smoothest are really covered with minute projec-
tions and depressions. These n't into each other, and a certain degree of
force is required to raise the projections of the one surface over those of the
other. With the naked eye we can not detect any unevenness on plate glass
or polished steel ; yet, if we view either through a microscope, we find that
its surface is far from smooth, and hence there is some friction even when
these substances are rubbed together.

183. Friction opposes motion in two ways:

1. By increasing the resistance, as when a weight is
dragged over the ground.

2. By diminishing the force before it is applied to the
resistance ; as in machinery, which sometimes loses as much
as one-third of its power by the rubbing of its different parts
against each other.

In estimating the working power of a machine for practical purposes, it
is necessary to make allowance for the loss occasioned by friction ; but, in
merely investigating the principles of Mechanics and the construction of ma-
chines, we proceed as if the surfaces concerned were perfectly smooth, and
no such thing as friction existed.

187. Kinds of Friction. There are two kinds of fric-
tion :

1. Sliding Friction, produced when a body slides on a

surface, like the runners of a sleigh.

2. Rolling Friction, produced when a body rolls on a

surface, like the wheels of a wagon.

188. Between any given surface and moving body, slid-
ing friction is much greater than rolling friction. Hence
we roll a barrel of flour over the ground instead of drag-

184. ITow are large amounts of work estimated ? What is meant by a ho^se-power T
Give an example. How may the horse-power of an engine be found? 185. By what
is the effect of the moving power often diminished ? What is Friction ? How is
it that friction is exhibited even between surfaces that appear smooth ? Give an ex-
ample. 1S6. In how many ways does friction oppose motion? Mention them. When
is it necessary to make allowance for friction, and when not? 1ST. How many kinrls
of friction are there? Name them, and tell how each is produced. 183. Between any



86



MECHANICS.



ging it, and place a weight that is to be moved in a cart, or
suspend it between wheels, instead of harnessing a horse
directly to it.



Fig. SO.



On the same principle, we place rollers under a block of marble, and fasten
castors, or small wheels, to the legs of heavy pieces of furniture. Rollers are

also used with advantage in pushing
a ponderous packing-box up an in-
clined plane into a cart, as shown in
Fig. 80. In all these cases, sliding
friction is converted into rolling, and
the resistance is thus diminished. The
larger the wheels and rollers employ-
ed, up to a certain limit, the greater
the gain ; but even small ones mate-
rially lessen the friction.

Rolling friction, on the other hand,
may be converted into sliding. This is done when the wheels of a heavily
loaded stage or wagon descending a steep hill are locked, that is, prevented
from turning by an apparatus provided for the purpose. The resistance is
thus increased to such a degree that the load can descend in safety. On the
same principle, brakes are applied to the wheels of cars, to stop them the
sooner.

189. Laws of Friction. Several important laws relating to friction have
been settled by experiments. In making these, the apparatus represented m




Fig. 81.



Fig. 81 has been used. D E is a table,
on which rests the block C. A string,
passing over the pulley B, connects this
block with a scale, A. By putting
weights in the scale till the block moves,
we are enabled to measure its friction ;
and, by making the block of different
materials, varying its size and surface,
and allowing it to remain a longer or
shorter time on the table, the following
laws have been established :

1. The friction of a body is greater when it commences
moving than after it has been moving for a time. Thus it




piven surface and moving body, how does sliding friction compare with rolling fric-
tion ? Mention some familiar cases in which we convert sliding into rolling friction,
to lessen the resistance. What is said of the size of the wheels and rollers employe 1 ?
In what cases is rolling friction converted into sliding? 189. How have the facts re-
lating to friction been settled ? Describe the apparatus employed for this purpose.
When is the friction of a, body greatest? Between what bodies and surfaces ia fric-



LAWS OF FRICTION. 87

takes a heavier weight to start the block C than it does af-
terwards to keep it in motion.

2. Friction is greater between soil bodies than hard
bodies, and between rough surfaces than smooth ones. A
sled that can hardly be moved over a newly ploughed field,
is drawn without difficulty over a frozen pond.

3. In many cases, friction is increased by letting the
surfaces remain in contact. At the end of five or six
days, it has been found to be fourteen times as great as at
first.

4. Between the same surfaces, friction is proportioned
to the weight of the moving body. The friction of a block
weighing 20 pounds is twice as great as that of a ten-pound
block.

5. Within certain limits, friction is not increased by ex-
tent of plane surface. As long as the weight of a body re-
mains the same, its friction will not vary, whether it rests
on a larger or smaller base. In Fig. 81, the block C has its
upper side hollowed out, so that, if turned over, it will rest
merely on two ridges ; yet the friction will be the same when
it rests on that side as on the other.

190. Modes of Lessening Friction. No means has yet
been found of doing away with friction altogether ; but it
may be lessened in three ways :

1. By smoothing and polishing the surfaces.

2. By putting grease or some other lubricant, as it is
called, between the surfaces. This fills up their depressions.
Finely powdered plumbago (the common black-lead used
in pencils), dry for wooden surfaces and mixed with grease
for metallic ones, is one of the best articles used for this
purpose. The wood-sawyer greases his saw to make it
move easily, and cartmen and carriage-drivers keep the

tion preatest ? In many cases, how may friction be increased ? Between the same
surfaces, to what is friction proportioned ? What effect is produced on the friction of
a body hy increasing its surface? Exemplify this with the figure. 190. Can friction
be entirely removed ? In how many ways may it be lessened ? What is the first of
these? What, the second? What article makes one of the best lubricants? By
Whom are lubricants used ? How may the friction, of a wheel be diminished ? What




88 MECHANICS.

axles of their wheels well covered
with some lubricating preparation.

3. The friction of a wheel may
be diminished by making its axle,
that is, the cylinder running through
the centre, turn on the circumfer-
ences of two other wheels at each
end, as shown in Fig. 82. Such
wheels are called Friction Wheels.
They are used in delicate machinery.

191. Uses of Friction. Though friction occasions a great loss of power,
It is not without its beneficial effects. A river is prevented from rushing
madly through its channel by the friction of its waters on its banks and bed.
A tempest gradually loses its force by the friction of the air against the pro-
jections on the earth's surface. It is friction that prevents the fibres of wool,
hemp, and cotton, when twisted together, from slipping on each other and
giving way. Without friction nails would be useless, for they would draw



Online LibraryG. P. (George Payn) QuackenbosA natural philosphy: embracing the most recent discoveries in the various branches of physics .. → online text (page 8 of 42)